Find the mass and the center of mass of the lamina occupying the region $R$, where $R$ is the triangular region with vertices $( 0,0 ) , ( 2,5 )$, and $( 4,0 )$, and having the mass density $\rho ( x , y ) = x$.
Select the correct answer.
A)
$m = 25 , ( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
B)
$m = 20 , ( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
C)
$m = 25 , ( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$
D)
$m = 20 , ( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$

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The Answer of Find the mass and the center of mass of the lamina occupying the region $R$, where $R$ is the triangular region with vertices $( 0,0 ) , ( 2,5 )$, and $( 4,0 )$, and having the mass density $\rho ( x , y ) = x$.
Select the correct answer.
A)
$m = 25 , ( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
B)
$m = 20 , ( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
C)
$m = 25 , ( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$
D)
$m = 20 , ( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$

Find the Mass and the Center of Mass of the Lamina